Step |
Hyp |
Ref |
Expression |
1 |
|
nsgsubg |
|
2 |
|
ghmpreima |
|
3 |
1 2
|
sylan2 |
|
4 |
|
ghmgrp1 |
|
5 |
4
|
ad2antrr |
|
6 |
|
simprl |
|
7 |
|
simprr |
|
8 |
|
simpll |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
9 10
|
ghmf |
|
12 |
8 11
|
syl |
|
13 |
12
|
ffnd |
|
14 |
|
elpreima |
|
15 |
13 14
|
syl |
|
16 |
7 15
|
mpbid |
|
17 |
16
|
simpld |
|
18 |
|
eqid |
|
19 |
9 18
|
grpcl |
|
20 |
5 6 17 19
|
syl3anc |
|
21 |
|
eqid |
|
22 |
9 21
|
grpsubcl |
|
23 |
5 20 6 22
|
syl3anc |
|
24 |
|
eqid |
|
25 |
9 21 24
|
ghmsub |
|
26 |
8 20 6 25
|
syl3anc |
|
27 |
|
eqid |
|
28 |
9 18 27
|
ghmlin |
|
29 |
8 6 17 28
|
syl3anc |
|
30 |
29
|
oveq1d |
|
31 |
26 30
|
eqtrd |
|
32 |
|
simplr |
|
33 |
12 6
|
ffvelrnd |
|
34 |
16
|
simprd |
|
35 |
10 27 24
|
nsgconj |
|
36 |
32 33 34 35
|
syl3anc |
|
37 |
31 36
|
eqeltrd |
|
38 |
|
elpreima |
|
39 |
13 38
|
syl |
|
40 |
23 37 39
|
mpbir2and |
|
41 |
40
|
ralrimivva |
|
42 |
9 18 21
|
isnsg3 |
|
43 |
3 41 42
|
sylanbrc |
|